I'm wondering if there are any passages/prophecies about salvation for the Gentile world in the Old Testament. If you know any, please share.
YES, there are!
The footnote in my NLT Bible for Acts 11:1 has a list of Old Testament verses that say that salvation is for all people, not just the Jews. Below, I've reproduced the list and for two of them, I've directly quoted them because they're the clearest and most direct with regards to this topic.
Isaiah 49:6 (NLT)
6 He says, “You will do more than restore the people of Israel to me.
I will make you a light to the Gentiles,
and you will bring my salvation to the ends of the earth.”
11 Many nations will join themselves to the Lord on that day, and they, too, will be my people. I will live among you, and you will know that the Lord of Heaven’s Armies sent me to you.
The first promise to the Gentiles was given to Adam and Eve (Gen.3:15) who were not Jews. The second promise was given to Japheth, the son of Noah who was father to the Gentiles (Gen.9:27).Shem was the father of the Jews (Gen.9:26). This was later confirmed by Isaiah (Isa.54). And I might add two more things. The word Jew was given to Israel by the Gentiles after the Tribe of Judah. The Jewish people are actually of Syrian decent according to Scripture (Due.26:5). As for praying for Israel we should pray as we do for all men but asking God to bless Israel is a sin. Note (2 John 2:7-11). Only those that are in Christ are of Israel "seed" (Gal.3:16) and (Gal.3:27-29). Let Gods Word be true and every man a liar that does not agree with it. God bless those that are in Christ the Son of God.